A turbomachine comprises one or more rotors formed of bladed wheels, that is to say of blades mounted on a moving disk rotating about an axis, and one or more cascades formed of bladed wheels that are stationary, that is to say not moving in rotation with respect to the above axis. The blades of the stationary and moving wheels over which a gaseous fluid passes in a direction generally parallel to the axis. One of the principal sources of excitation of the stationary or moving blades is due to the wakes and the pressure fluctuations generated by obstacles adjacent the blading. These various obstacles, namely the blades of stages upstream and downstream, or even the arms of the casing, lead to perturbations in the flow of fluid through the blading. Movement of the blades in these perturbations creates a harmonic excitation synchronous with the rotor's rotation speed and generates an unsteady pressure field on the surface of the blade.
In the field of aeronautical turbomachines, the bladings are particularly sensitive parts because their design must meet the requirements of aerodynamic performance, of aeroacoustics and of mechanical resistance to rotation, to the temperature and to aerodynamic load. These aspects together mean that these structures are under quite a high static load and that, taking account of lifetime requirements, the amplitudes of vibrations they are subjected to must remain low. Moreover, the aeroelastic coupling, that is the coupling between the dynamics of the bladed wheels and the fluid flow, determines the vibration stability of the structure.
Within the context of the design of a turbomachine, and taking account of the multidisciplinarity of the contributors, the design process is iterative. The vibration design work is carried out to avoid the presence of critical resonances in the machine's operational range. The assembly is validated at the end of the design cycle using a test engine on which the vibration amplitudes are measured. Sometimes there are high vibration levels linked either to resonances or to vibrational instabilities. The rotor concerned must then be readjusted, which is particularly time-consuming and expensive.